[10][11] After immigrating to the United States from the Dominican Republic, Peralta's father was employed as a bank teller.

[17] In the November 5, 2002 election, Peralta won a seat in the New York State Assembly representing District 39.

[21][22][23] The 39th Assembly District in New York was created in 2002 as a result of the significant increase in immigrant population in the region.

[21][24] Peralta was sworn in as a member of the Assembly by Civil Court Judge Diccia Pineda, also of Dominican heritage.

[26] In June 2007, Peralta was among a majority of the Assembly that voted to support passage of a same-sex marriage bill in New York.

[27] In January 2008, Peralta co-signed legislation with Sheldon Silver, Audrey Pheffer and Rory I. Lancman which put forth a proposal of $150 million in funding for families that had the possibility of their homes being foreclosed upon.

[30] Politician Hiram Monserrate was expelled from the Senate on February 9, 2010 by a 53–8 vote of his former colleagues after being convicted of misdemeanor assault on his girlfriend Karla Giraldo.

[29] Peralta became a candidate for the March 16, 2010 special election to fill the Senate seat left vacant due to Monserrate's expulsion.

[33] Peralta received the endorsement of the Empire State Pride Agenda (ESPA) due to his support for LGBT rights.

[42][43] In the September 2018 Democratic Party primary, Peralta was defeated by Jessica Ramos, a board member of the Jackson Heights Beautification Group.